The present invention relates generally to tissue removal techniques and, more particularly, to generating locations for scanning with a laser to achieve a desired ablation profile for correction of errors in vision during laser eye surgery.
A scanning system has the ability to trace out an arbitrary pattern with a small low energy spot. In most cases, a small spot equates to finer scanning details but at the expense of requiring more pulses to remove a given volume. The notion that a small spot will give a better fit than a large spot is generally true for arbitrary spot and ablation shapes, but the spot shapes can also affect the fit. For instance, trying to fit round disks into a square shape will result in a residue. The emphasis on getting a good fit should be on choosing a good balance of spot geometry and size.
Small spot scanners have their problems. A small spot will have smaller coverage per shot, thereby requiring more pulses to remove a given ablation volume (inversely proportion to the area of the spot size). A larger spot will require a substantially smaller number of pulses but at the expense of resolution. Understanding how treatment varies with spot overlap will ease our ability to create ablation patterns.
Present ablation algorithms follow a removal or subtractive process. An ablation spot is placed on a location along the two-dimensional corneal surface. This spot ablates a volume of tissue from the surface to produce a crater on this surface. Another spot is applied at another location along the two-dimensional corneal surface and another crater is produced. The challenge lies in placing the craters in the correct locations such that adding up the overlapping craters will produce the desired surface without producing undesirable residues and requiring excessive processing time.
The present invention relates to tissue ablation utilized in, for instance, corneal sculpting. In general, embodiments of the invention determine a treatment table containing scanning spot locations and characteristics (e.g., size, shape, and depth) for directing overlapping scanning spots of a laser beam to achieve a target ablation profile. Some embodiments of the invention use symmetry effects (e.g., axisymmetry or bilateral symmetry) to simplify the overlap analysis to determine scanning spot locations for directing the laser beam to achieve a desired ablation profile. In specific embodiments, the spot center locations define a series of linear overlapping ablation paths, with the shape of the ablation paths preferably being selected in response to a desired change in an optical characteristic of the eye. The scanning spots can be uniform or variable in size, shape, and/or depth. Advantageously, these paths can produce ablation treatment profile elements which can be combined, adjusted, and positioned over the two-dimensional corneal surface to, in combination, produce the desire three-dimensional sculpting. The ablation profiles of the overlapping paths can be represented by basis functions, which may include an array of ablation profile data or can be expressed analytically for certain profiles.
An aspect of the present invention is directed to a method of generating a treatment table for ablating tissue using a scanning laser beam for generating scanning spots over a treatment region larger in area than the scanning spots. The method comprises providing a target function or lens function representing a desired lens profile for ablating the tissue by scanning spots of the laser beam on the tissue. A basis function represents a treatment profile produced by the overlapping scanning spots in a treatment pattern. The target function is fitted with the basis function to obtain the treatment table including scanning spot locations and characteristics for the overlapping scanning spots of the laser beam. In a specific embodiment, the scanning spot locations are randomized to produce a random scanning order. The scanning spot characteristics of a scanning spot may include scanning spot size, shape, and depth of the scanning spot at a specific scanning spot location.
Any desirable treatment pattern for scanning with overlapping scanning spots of the laser beam may be specified. In some embodiments, the overlapping scanning spots define a treatment pattern in the form of, e.g., a linear path, and the basis function is a two-dimensional function representing a two-dimensional section of a three-dimensional treatment profile which has symmetry with respect to the two-dimensional section extending along the treatment pattern. For example, the treatment pattern is generally straight for myopic and hyperopic cylinders, and is generally circular for myopia and hyperopia. In a specific embodiment, the lens function represents an ablation depth as a function of a distance from an optical axis of a cornea. The basis functions of a series of offset patterns are combined, the profiles of laterally adjacent paths often overlapping to provide a smooth treated surface.
In some embodiments, the spot size and shape are generally fixed. In other embodiments, the spot size and shape are variable. The ability to achieve the desired ablation profile using fixed spot size and/or shape may allow the use of a more simplistic laser source and simplify the ablation process.
In specific embodiments, fitting the lens function with the basis function includes fitting at N discrete evaluation points. The basis function includes M discrete basis functions representing M overlapping scanning spots. The M discrete basis functions may represent M overlapping scanning spots across a treatment zone length representing the length across a generally two-dimensional section which is oriented normal across a generally straight treatment pattern or which is oriented radially across a generally circular treatment pattern.
For a treatment profile having a generally uniform two-dimensional section oriented normal across a generally straight treatment pattern, the discrete basis functions represent the two-dimensional section as
Xi(xj)=yi(xj)={square root over ((s/2)2xe2x88x92(xjxe2x88x92x0i)2)}; or, 
for a treatment profile having a generally uniform two-dimensional section oriented radially across a generally circular treatment pattern, the discrete basis functions represent the two-dimensional section as             X      i        ⁡          (              x        j            )        =                    θ        i            ⁡              (                  x          j                )              =                  cos                  -          1                    ⁡              (                                            x              j              2                        +                          x                              0                ⁢                i                            2                        -                                          (                                  s                  /                  2                                )                            2                                            2            ·                          x                              0                ⁢                i                                      ·                          x              j                                      )            
where
s is the diameter of the scanning spot;
j=1, . . . , N;
xj is a reference x-coordinate for the two-dimensional section measured from an optical axis of the cornea of a jth evaluation point for the center of the scanning spot;
x0i is an x-coordinate for a center of an ith scanning spot;
(x0ixe2x88x92s/2)xe2x89xa6xjxe2x89xa6(x0i+s/2);
yi(xj) is a depth of the ith basis function for the generally straight treatment pattern; and
xcex8i(xj) is a coverage angle of the ith basis function for the generally circular treatment pattern.
In a specific embodiment, fitting the lens function with the basis function comprises solving the following equation for coefficients ai representing treatment depth for the ith scanning spot:       f    ⁡          (              x        j            )        =            ∑              i        =        1            M        ⁢                  a        i            ⁢                        X          i                ⁡                  (                      x            j                    )                    
where
f(xj) is the lens function; and
i=1, . . . , M.
Fitting the lens function and the basis function may include specifying a deviation for each of the N discrete evaluation points. The method may include refitting the lens function with the basis function by varying the deviations to iterate for an acceptable fit or a best fit. The method may further include refitting the lens function with the basis function by varying the number of scanning spots M to iterate for a best fit. The method may also include refitting the lens function with the basis function by varying the size of the scanning spot and/or the number of scanning pulses at a scanning spot location to iterate for a best fit. A merit function may be defined to represent an error of fit between the lens function and the basis function. The method includes minimizing the merit function to achieve the best fit. In some embodiments, the merit function and the total number of scanning spots in the treatment table are both minimized to achieve the best fit with the least number of scanning spots.
Another aspect of the invention is directed to a method of generating scanning spot locations for ablating tissue using a scanning laser beam for generating scanning spots over a treatment region larger in area than the scanning spots. The method comprises providing a lens function representing a desired lens profile for ablating the tissue by scanning spots of the laser beam on the tissue. A basis function represents a treatment profile produced by the overlapping scanning spots along a treatment path. The basis function represents a section oriented across the treatment path. The lens function is fitted with the basis function to obtain the scanning spot locations for the overlapping scanning spots of the laser beam. In specific embodiments, the treatment profile is symmetrical with respect to an axis of symmetry.
In accordance with another aspect of the invention, a method for fitting a three-dimensional target profile comprises providing a two-dimensional basis function including overlapping portions to represent a three-dimensional profile which has symmetry with respect to a two-dimensional section extending along a treatment pattern. The three-dimensional target profile is fitted with the two-dimensional basis function to obtain a distribution of the overlapping portions.
In accordance with yet another aspect of the present invention, a system for ablating tissue comprises a laser for generating a laser beam, and a delivery device for delivering the laser beam to a tissue. A controller is configured to control the laser and the delivery device. A memory is coupled to the controller, and comprises a computer-readable medium having a computer-readable program embodied therein for directing operation of the system. The computer-readable program includes a first set of instructions for generating a treatment table for ablating the tissue over a treatment region larger in area than the spot size of the laser beam to achieve a desired lens profile for ablating the tissue, a second set of instructions for controlling the laser to generate the laser beam, and a third set of instructions for controlling the delivery device to deliver the laser beam to the tissue at the scanning spot locations.
In specific embodiments, the first set of instructions includes a first subset of instructions for providing a target function representing the desired lens profile for ablating the tissue by scanning spots of the laser beam on the tissue, a second subset of instructions for providing a basis function representing a treatment profile produced by the overlapping scanning spots in a treatment pattern, and a third subset of instructions for fitting the target function with the basis function to obtain the treatment table including scanning spot locations and characteristics for the overlapping scanning spots of the laser beam.